Automatically optimizing heuristics for robust scale-free network design via large language models

Achieving scale-free robust networks is a challenging problem due to its NP-hard nature and the vast, complex, high-dimensional solution space. Current methods, from handcrafted feature extraction to deep learning approaches, have made certain advancements but remain rigid and complex, often requiring manual design, trial and error, and large amounts of labeled data. To address these challenges, we propose AutoRNet, a novel framework that integrates large language models (LLMs) with evolutionary algorithms to generate complete heuristics for robust network design, supported by expert-crafted Network Optimization Strategies (NOSs). With the intrinsic properties of robust scale-free network structures in mind, NOS-based variation operations provide domain-specific prompts for LLMs, leveraging expert-defined domain knowledge to guide the creation of advanced heuristics. Moreover, to address the difficulty posed by the hard constraint of maintaining degree distributions, an adaptive fitness function is designed, progressively strengthening constraints to balance convergence and diversity. We evaluate the robustness of networks generated by AutoRNet's heuristics on both sparse and dense initial scale-free networks. These solutions outperform those from current methods. AutoRNet reduces the extent of manual heuristic design by utilizing structured domain knowledge through expert-crafted NOSs, offering a flexible and adaptive approach for generating robust scale-free network structures. The source code and dataset for this work have been made publicly available at https://github.com/leonyuhe/AutoRNet .